Question

Help me solve #15 please!!

Formulas if you need them:
RHOMBUS: A = 1/2 (d1)(d2)​

Answer 1

Area of the given rhombus = 498.83 ft²

Solution:

Given figure is a rhombus ABCD.

BE = 12 ft and ∠BAE = 30°

Property of rhombus:

Diagonals bisect each other at right angles.

In ΔAEB, ∠BAE = 30°, ∠AEB = 90° and BE = 12 ft

$\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\sin30^\circ=\frac{\text{BE}}{\text{AB}}$

$\frac{1}{2} =\frac{\text{12}}{\text{AB}}$

Do cross multiplication, we get

AB = 24 ft

Using Pythagoras theorem,

$\text {Adjacent}^{2}+\text{Opposite}^{2}=\text{ Hypotenuse }^{2}$

$AE^2+BE^2=AB^2$

$AE^2+12^2=24^2$

$AE^2+144=576$

$AE^2=432$

Taking square root on both sides, we get

$AE=12\sqrt{3}$ ft

AC = $2\times 12\sqrt{3}=24\sqrt {3}$

Area of the rhombus = $\frac{1}{2}\times d_1 \times d_2$

                                   $=\frac{1}{2}\times 24 \times 24\sqrt3$

                                   $=288\sqrt{3}$

                                   = 498.83 ft²

Area of the given rhombus = 498.83 ft²